What mass of glucose ( C_6H_ 12 O_6 ) must be dissolved in 500 g of...

Molality is defined as the number of moles of solute per kilogram of solvent.

$m = \dfrac{w \times 1000}{M \times W}$

Where $w$ is the mass of solute, $M$ is the molar mass of solute, and $W$ is the mass of solvent in grams.

Substituting the given values:

$0.2 = \dfrac{w \times 1000}{180 \times 500}$

$0.2 = \dfrac{w \times 2}{180}$

$0.2 = \dfrac{w}{90}$

$w = 18\text{ g}$

Answer: $18\text{ g}$